The Attention Budget: A Dynamics of Meaning-Systems Why a meaning-field has a master equation, in what currency it is paid, and how a system can starve with no one starving it

Abstract

Abstract The dynamics of a meaning-system requires a budget. Energy will not serve: meaning is not conserved, and there is no microscopic energy ledger from which a spiritual free energy could be defined. We argue that the budget is attention flux, and show that it satisfies the four conditions a budget must satisfy — bounded, rate-limited, carrying a minimum maintenance cost, and exactly the quantity contemporary information systems actually compete for. This version makes three corrections and three completions relative to the previous one. This version adds two further things. It states three theorems of the attention budget — conservation, devaluation, concealment — which stand in sequence rather than in parallel and which together answer the subtitle: conservation fixes what an allocation rule can and cannot move, devaluation names the lever, concealment says why the lever operates unopposed. And it makes the paper self-contained: it restates the three definitions it borrows and depends on no further result of the companion, so that the two papers are two independent branches of one subject rather than a paper and its appendix. Correction one: all three expenditures become multiplicative, and this strengthens two of the paper’s own results. The shock term was previously additive. Three independent reasons force the multiplicative form: a person already emptied cannot be further drained; attention not yet invested cannot be deactivated; a ritual no longer enacted loses nothing further to an external push. The first beneficiary is Corollary II: under the additive form a thin and a thick system pay the same shock cost, so the metaphor of a debt fails; under the multiplicative form the thick pays more and self-loading success stands. The second is the crisis criterion: the shock side now multiplies the stock, so an elaborate tradition takes a larger blow in the same crisis — which is precisely what the paper means to say and what its earlier expression could not deliver. Correction two: the Red-Queen number adopts the new definition, the dimensionless ratio of endogenous renewal to spontaneous loss; the old definition, with the shock in the numerator, would classify as active a system under heavy external interference that has entirely stopped renewing itself. Correction three: the minimum maintenance attention is rewritten accordingly. Completion one: the sign branch, and a prediction from it. Driving can push the meaning distribution to be more concentrated than the passive baseline — one grand narrative swallowing the rest — or more homogeneous — endless fragments, nothing mattering more than anything else. Both cost maintenance and their directions are opposite. Platforms push the homogeneous branch: they do not build a new religion, they flatten all meaning. And since work only amplifies the direction already present, an already fragmented environment fragments further with more investment. Completion two: the cognitive penalty, which gives the subtitle an information-theoretic answer. One volatility-to-drift ratio has three readings: the time average of the stock is docked by the ergodicity gap; the tail index of the distribution falls; and distinguishability falls, so one recognizes later that one has been emptied. The third is exactly what the subtitle asks — it is not that nobody is doing it, it is that distinguishability is too low for anyone to notice in time. Completion three: the active fraction and the degree of coupling are two sides of one quantity, where the previous version said only that they are related. Coordination cost is exactly the price of coupling, so the attention that carries it is exactly the attention that can build a we. The currency devaluation is therefore simultaneously a synchronization collapse: the same lever that empties the budget also unmakes the we the budget was meant to sustain.